67 research outputs found

    A containment result in Pn\mathbb{P}^n and the Chudnovsky conjecture

    Full text link
    In the paper we prove the containment I(nm)M(n1)mImI^{(nm)}\subset M^{(n-1)m}I^m, for a radical ideal II of ss general points in Pn\mathbb{P}^n, where s2ns\geq 2^n. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least 2n2^n points in Pn\mathbb{P}^n.Comment: 5 pages. To appear in PAM

    A vanishing theorem and symbolic powers of planar point ideals

    Full text link
    The purpose of this note is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We apply then this result in order to give a partial proof of a conjecture raised by Bocci, Harbourne and Huneke concerning containment relations between ordinary and symbolic powers of planar point ideals.Comment: 17 page

    Asymptotic Hilbert Polynomial and limiting shapes

    Full text link
    The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and S. Mayes established a connection between volumes of complements of limiting shapes and the asymptotic multiplicity for ideals of points. In the paper we prove a generalization of this fact to higher-dimensional sets

    Symbolic powers of planar point configurations

    Full text link
    We study initial degrees of symbolic powers of ideals of arbitrary finite sets of points in the projective plane over an algebraically closed field of characteristic zero. We show, how bounds on the growth of these degrees determine the geometry of the given set of points.Comment: 18 page

    Symbolic powers of planar point configurations II

    Full text link
    We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and we extend our considerations to the asymptotic setting of Waldschmidt constants. We introduce the concept of Bezout Decomposition which might be of independent interest.Comment: This article is a sequel to arXiv:1205.6002. 15 page

    Symbolic generic initial systems of star configurations

    Full text link
    The purpose of this note is to describe limiting shapes (as introduced by Mayes) of symbolic generic initial systems of star configurations in projective spaces over a field of characteristic 0.Comment: 8 page

    Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous ideals

    Full text link
    We study symbolic powers of bi-homogeneous ideals of points in the Cartesian product of two projective lines and extend to this setting results on the effect of points fattening obtained by Bocci, Chiantini and Dumnicki, Szemberg, Tutaj-Gasi\'nska. We prove a Chudnovsky-type theorem for bi-homogeneous ideals and apply it to classification of configurations of points with minimal or no fattening effect. We hope that the ideas developed in this project will find further algebraic and geometric applications e.g. to study similar problems on arbitrary surfaces.Comment: 12 pages, notes from a workshop on linear series held in Lanckoron
    corecore